By employing the surface and bulk micro-electro-mechanical system (MEMS) techniques, we design and demonstrate a simple and miniature optical Fabry-Perot interferometric pressure sensor, where the loaded pressure is gauged by measuring the spectrum shift of the reflected optical signal. From the simulation results based on a multiple cavities interference model, we find that the response range and sensitivity of this pressure sensor can be simply altered by adjusting the size of sensing area. The experimental results show that high linear response in the range of 0.2–1.0 Mpa and a reasonable sensitivity of 10.07 nm/MPa (spectrum shift/pressure) have been obtained for this sensor.
©2006 Optical Society of America
By employing the MEMS technology, a variety of optical MEMS pressure sensors based on Fabry-Perot interferometry have recently been proposed and fabricated [1–8]. The major advantages of the optical sensors over the conventional electrical sensors include the immunity to electromagnetic interference, resistance to harsh environment and capability for multiplexing. Fabry-Perot interferometer is an optical component consisting of two partially reflecting parallel mirrors separated by a gap. With this robust structure, one can easily measure a loaded pressure by detecting the changes of the reflected or transmitted optical signals due to the shift of this gap [1, 6–8].
Merits of the MEMS technology is proved in manufacturing the sensing elements with small and definite size. The measured response range, bandwidth, and sensitivity can be flexibly achieved by adjusting the size of sensing elements. In the previous works, different configurations of optical MEMS Fabry-Perot pressure sensors have been proposed, such as the ones using either a corrugated diaphragm  or single deeply corrugated diaphragm [5–6] to form the pressure-sensitive element, or the ones by bonding a planar diaphragm directly onto a polished fiber end face  or a Pyrex glass [7–8] surface where a hole is drilled for the inserted fiber. However, the high costs of manufacturing instruments as well as the complicated processing techniques are needed. To a certain extent, simplification to the sensing elements and their fabrication processes will be helpful for mass production and commercialization. The purpose of this paper is to present an optical MEMS pressure sensor which is fabricated by using the simplified micromachining techniques. Several methods are employed to simplify the fabrication process. A multiple cavities interference model for this sensor is introduced, which is used to analyze and design the optical sensing elements with composite membrane structures. In addition, the influences of silicon diaphragm thickness on the pressure response range and sensitivity are also analyzed in this paper.
2. Theory and modeling
As shown in Fig. 1, the pressure-sensing element consists of a glass plate and a silicon diaphragm where a deep cavity is anisotropically etched into the upper surface and a shallow cylindrical cavity is etched into the underside surface. Because the refractive indexes of the optical fiber, glass, air, silicon, and pressure medium are different, the light is coupled into the pressure sensor through optical fiber and reflected by each interface. The light interfered in multiple media is then coupled out of the sensor through the same optical fiber. The width of the air gap varies along with the loaded pressure due to the deflection of the silicon diaphragm. Since there exists a close relation between the width of the air gap and the reflection spectrum, it is expected that one can easily know the loaded pressure by measuring the spectrum shifts.
2.1. Interference model
As we know from the principle of elasticity , the deflection ω(r) of diaphragm due to a loaded pressure p is given by
where r is the distance from the deflected position to the central axis of diaphragm, ω0 is the deflection of the center position of diaphragm, R0 is the radius of silicon diaphragm, E is Young’s modulus, υ is Poisson’s ratio, and h is the thickness of silicon diaphragm thickness. The air cavity depth L of the sensor is a function of the maximum diaphragm deflection ω defined as
where L0 is the initial air cavity depth.
Figure 2 shows the interference model of the proposed pressure sensor._Because refractive indexes of the optical fiber and glass are different, the optical reflectivity at the interface of them cannot be ignored. r 1 r 2, r 3 and r 4 are the reflectivity at the four interfaces, respectively. Considering the practical situation, we define the coupling efficiency for the reflected lights at the interface of glass-air, air-silicon and silicon-pressure medium as η1, η2 and η3, respectively . By using the interference principle of thin film [10–12], the complex reflectivity r1′ is expressed as
Where ϕ 1 =φ 1,ϕ 2 =φ 1+φ 2,ϕ 3 = φ 1+φ 2+φ 3 , φi = 4∙πni Li/λ, is the round-trip phase shift in each medium, ni is refractive index, Li is the length of each layer, and
Here we have κi≪1, because the reflectivity of each interface is low. Then the equivalent reflectivity can be written as
Typical numerical results for the dependence of the equivalent reflectivity on the wavelength are shown in Figs. 3 and 4 respectively. As shown in Fig. 3, when a pressure is loaded, the phase difference in the air gap will vary and thus the reflected optical spectrum is shifted. Note that there is a higher frequency signal superposed on the lower frequency signal. When thickness of the glass reduces from 500 μm to 250 μm, it can be found from Fig. 4 that the frequency becomes half of the one. This result means that the signal with high frequency is due to the optical interference occurred at the surface of the glass. Although the multiple cavities interference method would demand more complicated signal process than the single- cavity one , this pressure sensor can be fabricated easier by using simplified micromachining techniques.
2.2. Sensitivity and response range
The thickness and radius of silicon diaphragm are two of the key parameters which will strongly affect the sensitivity and the pressure response range. Parameters of the glass and silicon diaphragm are kept constant during the operation of sensor, therefore change of the air gap is only considered in the following analysis. When light is transmitted from the air-glass interface to the air-silicon interface and is reflected back to the air-glass interface, the optical phase difference is given by
where nair is the refractive index and L is the air-gap length. Since φm is equal to 2mπ (a constant) for a certain resonant wavelength λm, taking a differentiation with respect to λ in Eq. (6), one can obtain
From Eq. (6), we approximately have
where P0 is arbitrarily defined in the range of the measured pressure. Since there exists a close relation between the change of φ2 and the shift of reflected optical spectrum, Δφ2/ΔP can be approximately used to explain the relation between the pressure sensitivity and the size of diaphragm. Moreover, nair and λm (P0) are constant in Eq. (9), the relative pressure sensitivity is defined as Se and can be approximated as
From Eq. (10), it is seen that the higher relative pressure sensitivity Se can be obtained by enlarging the radius of silicon diaphragm and reducing the thickness of silicon diaphragm. Since the response range is corresponding to 2π phase difference, according to Eqs. (1) and (8) we have
Eq. (11) indicates that a thicker silicon diaphragm and a smaller radius of diaphragm can give a wider response range ΔP max.
3. Fabrication of the sensing elements
In our work, surface and bulk MEMS techniques are used to fabricate the sensing elements. Figure 5 shows the processing steps. We have used a 4 inch silicon wafer and a Pryrex7740# glass wafer for silicon-glass anodic bonding. The thickness of silicon wafer is 450 μm and its orientation is <100>.
We start with making the oxidation (SiO2) and deposition of the silicon nitride (Si3N4) on the surface of the silicon wafer by using low pressure chemical vapor deposition (LPCVD) process [Fig. 5(a)]. Then we employ the reactive ion etch (RIE) and lithography technique to remove the SiO2 and Si3N4 on the underside of the wafer and selectively open a window on the upper side which is protected by a thick photoresist [Fig. 5(b)]. This etching technique is also selectively used to obtain shallow circular cavity [Fig. 5(c)] for the Fabry-Perot interferometer. The shallow circular cavity and the opened window are fabricated on the same silicon wafer, therefore double-face alignment for the silicon and glass wafers is not needed here. The fabricated wafer is anodically bonded onto the Pyrex 7740 glass wafer [Fig. 5(d)]. A potassium hydrate (KOH) anisotropic etching is performed to obtain silicon diaphragm whose thickness is monitored by using a surface profiler instrument. Size of the quadrate window is designed to be 2×2 mm2 to reduce the difficulty of double-face alignment. A magnetic force stirrer is used to mix round the KOH solution to keep the uniformity of silicon thickness.
Finally, the formed sensing arrays are cut into individual ones using a standard dicing saw. The fabricated structure and the fiber are packaged with epoxy method. Cavity depth between silicon diaphragm and the Pyrex glass is 4.6 μm. Thickness of this Pyrex glass is 500 μm. Radius of the cavity is 600 μm and the diaphragm thickness is about 40 μm. The uniformity of the diaphragm thickness is less than 0.5%.
4. Experimental results and discussions
Pressure tests have been carried out by employing a set-up illustrated in Fig. 6. The system consists of a broadband amplified spontaneous emission (ASE) light source (OPLINK, USA), a 2×2 coupler, an optical spectrum analyzer (AQ6317C, Ando, Japan), single mode fibers and index matching liquid. Besides, the pressure calibration was implemented by using a standard pressure meter with a pressure resolution of 0.02%.
The measured spectrum of the input ASE light source and the reflected spectrums from the sensor are shown in Figs. 7(a) and 7(b), respectively. The results as shown in Fig. 7(b) show that a complex interference in each different medium of the sensor is occurred as expected from the simulation results. Once the loaded pressure is changed, the spectrum will be shifted as shown in Fig. 7(c). Here low-pass filter method is used to eliminate the influence of the inserted glass on the reflected signal and to obtain quasi sinusoid optical spectrum signal as shown Fig. 7(c). The pressure calibration was carried out by measuring the spectrum shift. A straight line cl shown in Fig. 7(c) is selected to maximize the linearity and linear response range, where it intersects the spectrum curve at point A and B. Distance between point A and B indicates the shift of optical spectrum due to the loaded pressure.
Figure 8 shows a typical measuring result for the dependence of the loaded pressure on the shifted wavelength. It is found that a good linearity with less than 0.27 nm standard deviations for the present sensor can be obtained. The sensitivity (i.e., change in wavelength/loaded pressure) and response range of this pressure sensor were estimated to be 10.07 nm/MPa and 0.2 Mpa to 1.0 MPa, respectively. Moreover, the sensitivity can be improved by decreasing the thickness of silicon diaphragm. Since the wavelength precision of the OSA is 0.01 nm, it is therefore expected that the minimum detectable pressure alteration is 0.99 kpa in our set-up.
Note that, an optical spectrum analyzer (OSA) is used in our set-up for measuring the reflection spectrum shift. However, in the practical application, this measurement may be realized by using the general interrogation method without an OSA .
An optical MEMS pressure sensor based on the principle of Fabry–Perot interferometry has been demonstrated in this paper. The simplified micromachining techniques have been used to fabricate the pressure sensor. The multiple cavities interference model is applied to analyze the operation principle of the proposed sensor. Low-pass filter method has been used to eliminate the harmonics influence of optical spectrum signal resulted from the multiple cavities interference. Analysis results show that pressure response range and sensitivity can be flexibly achieved by adjusting the size of sensing element. The shift of the reflected optical spectrum is used to measure the loaded pressure and the minimum detectable pressure alteration of the tested sensor is 0.99 kpa. The sensitivity and response range of this sensor are experimentally characterized to be 10.07nm/MPa (spectrum shift/pressure) and 0.2–1.0 MPa, respectively. However, the temperature dependency of the sensor needs to be addressed in the future.
This work was supported by the National Natural Science Foundation of China, the Specialized Research Fund for the Doctoral Program of Higher Education (20050319007) and Jiangsu province high-novel technology project (BG2003024). The authors also thank Prof. K. Ogusu for his valuable suggestions.
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